\[\large { \frac{\log {\color{red}a}}{{\color{green}b}-{\color{blue}c}}} {\color{brown}=}\frac{\log{ \color{green}b}}{{\color{blue}c}- {\color{red}a}} {\color{brown}=}\frac{\log {\color{blue}c}}{{\color{red}a}-{\color{green}b}}\]

\( a, b, c \) are distinct positive real numbers that satisfy the above equation. What is

\[\large {{\color{red}a}^{\color{red}a} \times {\color{green}b}^{\color{green}b} \times {\color{blue}c}^{\color{blue}c}} = \ ? \]

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